Cancellation and Non Cancellation Phenomena for Infinite Complexes

Abstract

Let L(I, J) be defined by the pull-back of CP_∞l → K(+Q_, 2) ← _Ω SJ_3 where {I, J} is a partition of all primes. We classify spaces {Ωk Σk C(f)} of loop-suspension of mapping cone of phantom map f:L(l, J) → _S_3 for k = 0, 1, ⋯, ∞ which have the same n-type for all n. In the category of finite CW-complexes, cancellation and non cancellation phenomena are well studied. In the category of infinite CW-complexes, the phenomena are less known. We study cancellation and non cancellation phenomena for infinite dimensional complexes by using above spaces.